Date of Award

Spring 2021

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Public Health

First Advisor

Ma, Shuangge

Abstract

Despite significant main effects of genetic and environmental risk factors have been found, the interactions between them can play critical roles and demonstrate important implications in medical genetics and epidemiology. Although many important gene-environment (G-E) interactions have been identified, the existing findings are still insufficient and there exists a strong need to develop statistical methods for analyzing G-E interactions. In this dissertation, we propose four statistical methodologies and computational algorithms for detecting G-E interactions and one application to imaging data. Extensive simulation studies are conducted in comparison with multiple advanced alternatives. In the analyses of The Cancer Genome Atlas datasets on multiple cancers, biologically meaningful findings are obtained. First, we develop two robust interaction analysis methods for prognostic outcomes. Compared to continuous and categorical outcomes, prognosis has been less investigated, with additional challenges brought by the unique characteristics of survival times. Most of the existing G-E interaction approaches for prognosis data share the limitation that they cannot accommodate long-tailed or contaminated outcomes. In the first method, we adopt the censored quantile regression and partial correlation for survival outcomes. Under a marginal modeling framework, this proposed approach is robust to long-tailed prognosis and is computationally straightforward to apply. Furthermore, outliers and contaminations among predictors are observed in real data. In the second method, we propose a joint model using the penalized trimmed regression that is robust to leverage points and vertical outliers. The proposed method respects the hierarchical structure of main effects and interactions and has an effective computational algorithm based on coordinate descent optimization and stability selection. Second, we propose a penalized approach to incorporate additional information for identifying important hierarchical interactions. Due to the high dimensionality and low signal levels, it is challenging to analyze interactions so that incorporating additional information is desired. We adopt the minimax concave penalty for regularized estimation and the Laplacian quadratic penalty for additional information. Under a unified formulation, multiple types of additional information and genetic measurements can be effectively utilized and improved identification accuracy can be achieved. Third, we develop a three-step procedure using multidimensional molecular data to identify G-E interactions. Recent studies have shown that collectively analyzing multiple types of molecular changes is not only biologically sensible but also leads to improved estimation and prediction. In this proposed method, we first estimate the relationship between gene expressions and their regulators by a multivariate penalized regression, and then identify regulatory modules via sparse biclustering. Next, we establish integrative covariates by principal components extracted from the identified regulatory modules. Last but not least, we construct a joint model for disease outcomes and employ Lasso-based penalization to select important main effects and hierarchical interactions. The proposed method expands the scope of interaction analysis to multidimensional molecular data. Last, we present an application using both marginal and joint models to analyze histopathological imaging-environment interactions. In cancer diagnosis, histopathological imaging has been routinely conducted and can be processed to generate high-dimensional features. To explore potential interactions, we conduct marginal and joint analyses, which have been extensively examined in the context of G-E interactions. This application extends the practical applicability of interaction analysis to imaging data and provides an alternative venue that combines histopathological imaging and environmental data in cancer modeling. Motivated by the important implications of G-E interactions and to overcome the limitations of the existing methods, the goal of this dissertation is to advance in methodological development for G-E interaction analysis and to provide practically useful tools for identifying important interactions. The proposed methods emerge from practical issues observed in real data and have solid statistical properties. With a balance between theory, computation, and data analysis, this dissertation provide four novel approaches for analyzing interactions to achieve more robust and accurate identification of biologically meaningful interactions.

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